38 citations · 150 across the 39 of their papers we have counts for
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Deep Level-set Method for Stefan Problems
Mykhaylo Shkolnikov, H. Mete Soner, Valentin Tissot-Daguette
We propose a level-set approach to characterize the region occupied by the solid in Stefan problems with and without surface tension, based on their recent probabilistic reformulat…
Stefan problem with surface tension: uniqueness of physical solutions under radial symmetry
Yucheng Guo, Sergey Nadtochiy, Mykhaylo Shkolnikov
We study the Stefan problem with surface tension and radially symmetric initial data. In this context, the notion of a so-called physical solution, which exists globally despite th…
Well-posedness of the supercooled Stefan problem with oscillatory initial conditions
Scander Mustapha, Mykhaylo Shkolnikov
We study the one-phase one-dimensional supercooled Stefan problem with oscillatory initial conditions. In this context, the global existence of so-called physical solutions has bee…